UTI analysis

Michele Gubian

April 24, 2025

Motivation

Static analysis

  • Dataset contains many tongue contours like this
    • e.g. all contours at gesture mid-time
  • One “data point” is a whole contour
  • knots (1-11) are provided by UTI post-processing software
  • Static analysis = no time involved
  • GOAL: statistical analysis
    • e.g. how contour shape varies with respect to conditions A and B

Dynamic analysis

  • Dataset contains many sequences of tongue contours like this
    • e.g. contour sequences represent gestures form onset to offset
  • One “data point” is a sequence of contours, or a clip
  • Dynamic analysis = time axis should be included in the model
  • GOAL: statistical analysis
    • e.g. how dynamic gesture varies with respect to conditions A and B

Roadmap

  • Static or dynamic?
    • i.e. do we need the time axis?
  • Choose geometrical parametrisation of contours
    • radial coordinates
    • 2-dim. trajectory
  • Choose statistical modelling framework
    • GAMs
    • FPCA + LMER

Parametrization
- static case

y ~ x: a bad idea

  • Non-unicity of y values at a given x!

radius ~ angle

radius ~ angle

Flat version

Radial version

radius ~ angle: PROS

  • Simplest geometry
    • one indep. variable: angle
    • one dep. variable: radius
  • Plugs in to simplest model
  • Solves most of the non-unicity issues

radius ~ angle: CONS

  • Non-unicity at curled tongue tip
  • Requires choosing origin
  • Does not use knots properly

Interpolation

Flat version

Radial version

Linear angle normalization

Flat version

Radial version

Procrustean angle interpolation

Flat version

Radial version

(x, y) ~ knot

(x, y) ~ knot: PROS

  • Solves all non-unicity problems
  • Proper use of knots

(x, y) ~ knot: CONS

  • Complex model:
    • Two equations, one for x, one for y
    • Requires multivariate models

Parametrization
- dynamic case

radius ~ angle * time

radius ~ angle * time

Flat version

Radial version

radius ~ angle * time

  • Simplest geometry
  • Yet requires a 2D support
  • Same pros & cons as static counterpart

(x, y) ~ knot * time

(x, y) ~ knot * time

  • The most complex geometry
    • 2D support (knot, time)
    • 2 response variables (x, y)
  • Requires most complex models
  • All pros and cons of static counterpart